Vassia Atanassova

In the present paper, we introduce a new directional operation on intuitionistic fuzzy pairs and study some of its properties. For distinct inputs, the operation extrapolates from the first through the second to the triangle’s perimeter. We provide an explicit formula and illustrate the possible geometric configurations. An accompanying interactive software application supports visualization and numerical exploration of the construction.

The paper presents data and analysis of the blood group distributions of the Bulgarian population for the year 2024, retrieved from the national information system serving the centres and departments of transfusion haematology. Several significant indicators are considered in both national and regional aspects and in both absolute numbers and percentages. The study is particularly focused on tracing the ABO system blood type frequencies, Rh(D) antigen (rhesus factor) frequencies and certain demographic indicators of blood donation activity, including blood donor's sex, age, location and type of donation (voluntary or family/replacement). The atomic approach towards data analysis, adopted as early as the research planning phase, has given vast opportunities for data stratification in various ways and for discovering patterns, regional specifics and even data anomalies. The presented data and conclusions can serve in planning the operation and resources of the centres and departments of transfusion haematology on national and regional levels, for information backup of the blood donation campaigns and for raising the society's awareness and sensibility towards the needs and benefits of voluntary blood donation as the safest and most sustainable source of blood supply. This article is part of the theme issue ‘Data driven modelling for living systems’.

In recent decades, multicriteria analysis methods have been increasingly used in decision-making in the field of medicine. In this work, we present a modification of an established approach for this purpose—InterCriteria Analysis. In the new algorithm, the determination of the similarity in behaviour between pairs of criteria is based on the relations of the respective pairs of objects to the mean values of the respective criteria. The proposed modification of InterCriteria Analysis was applied to a dataset of 276 prostate cancer patients (obtained from a retrospective study). The obtained results for positive and negative consonance between the studied criteria are confirmed by reports in authoritative literature sources in the field of urology. The registered potential of the new method for detecting relationships between investigated criteria enables its application both independently and in combination with other methods of multicriteria analysis. This article is part of the theme issue ‘Data driven modelling for living systems’.

Continuing the research from four previous papers of the authors, here we check the validity of the two tautologies from the two tautologies of propositional logic ((A → B) & (A → C)) → (A → (B & C)), ((B ∨ C) → A) → ((B → A) ∨ (C → A)) and give the list of the intuitionistic fuzzy implications that satisfy these two formulas.

The paper proposes a completely new geometric interpretation of intuitionistic fuzzy sets for confidence-aware decision making. Instead of directly using ordered pairs of membership and non-membership degrees, we reinterpret the intuitionistic fuzzy triangle as a structured coordinate framework that simultaneously represents the evaluation outcomes and the evaluators’ expertise in the following manner: experts’ confidence levels are modelled with line segments parallel to the hypotenuse, while evaluation scores are represented by line segments radiating from the origin of the coordinate system toward the hypotenuse. Their intersections form a finite lattice of points whose total number depends on the chosen confidence and assessment scales. The proposed construction preserves the semantic foundations of intuitionistic fuzziness: points closer to the origin reflect higher uncertainty in the evaluator’s confidence, while points onto the hypotenuse represent determinate judgments (with varying degrees of positivity or negativity) based on the complete evaluator’s confidence. The geometric distances between intersections provide a formal explanation of varying discriminative power: assessments from highly confident reviewers are more distinguishable than those from less confident ones. In addition, a colour-based visualization further supports the intuitive interpretation of confidence-weighted evaluations. The proposed framework offers an alternative yet fully consistent way to model expertise-dependent decision processes within the intuitionistic fuzzy setting, bridging geometric insight and practical evaluation scenarios via a structured system of parallels and meridians.

Index matrices are an extension of the ordinary matrices with explicitly assigned index sets on both their rows and columns, forming an advanced mathematical structure used for specialized data modeling and problem-solving. In the present paper, a new operator, called “Inverse” operator, is defined over hierarchical index matrices with a description of its software implementation. This operator has no analogue in the classical theory of matrices. Its application allows various restructuring of datasets with multiple criteria, in order to outline data stratifications in the best possible way serving the particular decision maker’s needs. As an illustrative example for the new operator, a dataset of the recorded blood donors in Bulgaria is provided, with discussions of the different stratifications and perspectives in which the dataset can be rearranged using the “Inverse” operator.

We consider four new geometrically motivated operators acting in the interior of the interpretation triangle used to depict intuitionistic fuzzy sets. The first operators uses the points resulting from the classical "necessity" and "possibility" operators, in combination with the point ⟨0, 0⟩. The definition of the second operator employs the projections of the considered point onto the sides of the triangle, as viewed from the vertices ⟨0, 0⟩, ⟨0, 1⟩, and ⟨1, 0⟩. The remaining two operators combine two of these projections with the result of the modal operators of the internal point. We also consider operators obtained as linear combinations of some of these four operators.

In the present paper we investigate the relationship between intuitionistic fuzzy sets, interval-valued intuitionistic fuzzy sets and some proposed extensions of fuzzy sets, intuitionistic fuzzy sets, and sets that have similar structure. In many cases we establish that the proposed concepts claiming to be extensions of the intuitionistic fuzzy sets are either incorrect in their definitions or offer nothing new compared to the already existing notions. Finally, we formulate four requirements that must be observed so that a new concept claiming to extend an existing one can be considered legitimate and viable, expanding the boundaries of the existing mathematical theory in a meaningful way.

Intuitionistic fuzzy sets (IFSs), proposed in 1983, are one of the most viable and widely explored extensions of Zadeh’s fuzzy sets. In the decade following their introduction, they were extended to interval-valued IFSs (IVIFSs), temporal IFSs, IFSs of the second type (incorrectly called “Pythagorean fuzzy sets” by some authors) IFSs of n-th type, and IFSs over different universes. For each of these extensions, at least one geometrical interpretation has been defined, and for IVIFSs, at least seven different interpretations are known. In the present paper, revisiting some existing results on IVIFSs, some necessary modifications, additions, and corrections to the planar and spatial geometrical interpretations are introduced here for the first time. A new, eighth, geometrical interpretation of IVIFSs is proposed. A basic logic operation and two modal operators are illustrated and a comparison is made between the planar and the new “two-rods” geometrical interpretations of identical IVIFS elements. Finally, a new operator over IVIFSs is proposed for the first time, some of its properties are proven, and its geometrical interpretations are described.